Question

3. If the ratio of A to B is 3 : 2 and the ratio of B to C is 3:2, find
the ratio A:B: C. Are A, B, C are in continued proportion?​

Answer 1

Answer:

9:6:4 this is the correct answer

Answer 2

Answer:

How to Solve Proportions?

• It is easy to calculate if ratios are proportional. To check if the ratio a: b and c: d is proportional.

• Multiply the first term with the last term: a x d
• Multiply the second term with the third term: b x c
• If the product of extreme terms is equal to the product of mean terms, then the ratios are proportional: a x d = b x c

Continued proportion

• Two ratios a: b and b: c is said to be in continued proportion if a: b = b: c. In this case, the term c is called the third proportion of a and b whereas b is called the mean proportion of between the terms a and c.

• When the terms a, b and c are in continued proportion, the following formula is derived:

• a/b = b/c

• Cross multiplying the terms gives; a x c =b x b, Therefore,

b² = ac

Step-by-step explanation:

Example 1

Find out if the following ratios are in proportion: 8:10 and 12:15.

Explanation

Multiply the first and fourth terms of the ratios.

8 × 15 = 120

Now multiply the second and third term.

10 × 12 = 120

Since the product of the extremes is equal to the product of the means,

Since, the product of means (120) = product of extremes (120),

Therefore, 8: 10 and 12:15 are proportional.

Example 2

Verify if the ratio 6:12::12:24 is proportion.

Explanation

This is a case of continued proportion, therefore apply the formula a x c =b x b,

In this case, a: b:c =6:12:24, therefore a=6, b=12 and c=24

Multiply the first and third terms:

6 × 24 = 144

Square of the middle terms:

(12) ² = 12 × 12 = 144

Therefore, the ratio 6:12:24 is in proportion.

Example 3

If 12:18::20: p. Find the value of x to make the ratios proportional?

Explanation

Given: 12: 18::20: p

Equate the product of extremes to the product of means;

⇒ 12 × p = 20 × 18

⇒ p = (20 × 18)/12

Solve for p;

⇒ p = 30

Hence, the value of p= 30

Example 4

Find the third proportional to 3 and 6.

Explanation

Let the third proportional be c.

Then, b² = ac

6 x 6 = 3 x c

C= 36/3

= 12

Thus, the third proportional to 3 and 6 is 12

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